Interactions between the octet-baryons (B₈) in the spin–flavor SU₆ quark model are investigated in a unified coupled-channels framework of the resonating-group method (RGM). The interaction Hamiltonian for quarks consists of the phenomenological confinement potential, the color Fermi–Breit interaction with explicit flavor-symmetry breaking (FSB), and effective-meson exchange potentials of scalar-, pseudoscalar- and vector–meson types. The model parameters are determined to reproduce the properties of the nucleon–nucleon (NN) system and the low-energy cross section data for the hyperon–nucleon interactions. Mainly due to the introduction of the vector mesons, the NN phase shifts at non-relativistic energies up to are greatly improved in comparison with the previous quark-model NN interactions. The deuteron properties and the low-energy observables of the B₈B₈ interactions, including the inelastic capture ratio at rest for the Σ⁻p scattering, are examined in the particle basis with the pion-Coulomb correction. The nuclear saturation properties and the single-particle (s.p.) potentials of B₈ in nuclear medium are examined through the G-matrix calculations, using the quark-exchange kernel. The Σ s.p. potential is weakly repulsive in symmetric nuclear matter. The s.p. spin–orbit strength for Λ is very small, due to the strong antisymmetric spin–orbit force generated from the Fermi–Breit interaction. The qualitative behavior of the B₈B₈ interactions is systematically understood by (1) the spin–flavor SU₆ symmetry of B₈, (2) the special role of the pion exchange, and (3) the FSB of the underlying quark Hamiltonian. In particular, the B₈B₈ interaction becomes less attractive according to the increase of strangeness, implying that there exists no B₈B₈ di-baryon bound state except for the deuteron. The strong ΛN–ΣN coupling results from the important tensor component of the one-pion exchange. The ΛΛ–ΞN–ΣΣ coupling in the strangeness S=−2 and isospin I=0 channel is relatively weak, since this coupling is caused by the strangeness exchange. The B₈B₈ interactions are then applied to some of the few-baryon systems and light Λ-hypernuclei in a three-cluster Faddeev formalism using two-cluster RGM kernels. An application to the three-nucleon system shows that the quark-model NN interaction can give a sufficient triton binding energy with little room for the three-nucleon force. The hypertriton Faddeev calculation indicates that the attraction of the ΛN interaction in the state is only slightly more attractive than that in the state. In the application to the ααΛ system, the energy spectrum of is well reproduced using the αα RGM kernel. The very small spin–orbit splitting of the excited states is also discussed. In the ΛΛα Faddeev calculation, the NAGARA event for is found to be consistent with the quark-model ΛΛ interaction.